Generalized Voronoi Diagrams

Generalized Voronoi Diagrams (GVDs) have far-reaching applications in robotics, visualization, graphics, and simulation. However, while the ordinary Voronoi Diagram has mature and efficient algorithms for its computation, the GVD is difficult to compute in general, and in fact, has only approximation algorithms for anything but the simplest of datasets. Our work is focused on developing algorithms to compute the GVD efficiently and with bounded error on the most difficult of datasets -- those with objects that are extremely close to each other.